A Theory of Optical Second Harmonic Generation Via Symmetry and Group-Theoretic Methods in Mechanics

Abstract

Based on classical Lorentz theory of electrons, one can construct anisotropic coupled equations of motion of anharmonic Lorentz oscillator, which conform to crystal symmetry operations. The solution of the aforementioned coupled equations yields second harmonic component when the driving electric field contains fundamental harmonic only. The physical model of this theory is that electrons oscillate simultaneously and sinusoidally in the xy plane with frequency ω and along the z-direction with frequency 2ω.